BROOKLYN, N.Y. — For a guy who thrives at the cutting edge of jazz, Ethan Iverson is mighty fixated on history. It’s part philosophical — to make great new music, he believes, requires a profound understanding of the music of the past. And it’s part selfish. Iverson, a pianist best known as one third of the iconoclastic trio The Bad Plus, writes a scholarly and well-loved blog called Do The Math, and he likens his deep historical dives (transcribing 30 Bud Powell recordings, for instance, before penning a four-part, 15,000-word essay) to taking his morning vitamins.

Then there’s the simple fact that, at 43, Iverson has already realized his big musical dream.

“I wanted to play music that I’ve never heard before,” he says, “and in The Bad Plus that was achieved. So in terms of my personal journey, the obvious next step for me was to look at the masters. That’s what I’m into. That’s what I’m dealing with every day in my personal practice.”

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That’s also what he’ll bring to his new teaching gig at New England Conservatory, so heads up, students. Your professor has no intention of teaching you about his creative process. Iverson is here to help you understand what it is you want to do — and, critically, whatever that thing is, how to practice it.

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“I think everybody wants to be a John Cage or an Ornette Coleman level of individual genius. I did, too, at that age. But the practical matter is you’re probably not at the NEC Jazz Program if you are. So you’re probably dealing with the text, and if that’s the case, I can help. I’ve thought a lot about how you can shape it to your own desires.”

Beyond that, Iverson says, “jazz in the classroom is some kind of malarkey.”

The man doesn’t mince words. Or notes. His are concise, eye-opening, clear as water but never conventional. It’s hard to think of a musician whose playing is at once so elegant and so transgressive.

“Ethan is a bit of a paradox,” says the saxophonist Joshua Redman, who made an album with The Bad Plus last year. “His knowledge of the jazz language and tradition may be without parallel in his generation, but he’s not a traditionalist as a player. He’s attracted to music that feels to him unknowable.”

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Mystery can’t be rushed, and Iverson has always known it. When he was 20, at a time of life when most gifted young players are racing to get a record deal, Iverson impressed Fred Hersch — his first New York piano teacher and the retired NEC professor he is succeeding — by telling him that he was in no hurry to make it. To this day, patience is Iverson’s defining musical quality.

“Yes, traditionally I play much slower than my peers,” he says. “I always wanted to make sure I had a belief in every note.”

He paid his $300 monthly rent accompanying singers on auditions, playing in a tango band and with a sports comedy group, and eventually as music director for the Mark Morris Dance Group. When Iverson, drummer Dave King, and bassist Reid Anderson, Midwesterners all, formed The Bad Plus, the pianist gamely agreed to flesh out the trio’s skimpy set of originals at their first gig with a Nirvana tune, even though he had zero interest in popular music.

“At that first rehearsal I was like, ‘Man, this is really something,’” Iverson recalls. “‘This is a very unique emotion. I for sure have never heard this before.’” Sixteen years later, he still sounds startled.

The Bad Plus has become famous for its radical deconstructions of rock songs, from Aphex Twin and ABBA to Neil Young and Blondie. Since 2001 the group has toggled between cover tunes and knotty originals, throwing in an ambitious reimagining of Stravinsky’s The Rite of Spring. Last month The Bad Plus released “It’s Hard,” a set of covers named after a song by the Who that doesn’t appear on the album. Huh? “I don’t know what to say,” Iverson says. “I have answers, but the more you explain some of these things the less potential they have.”

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Less is more in Iverson’s world, except when it’s not. He refrains from cooking, gardening, heavy lifting, and athletics. A pianist’s hands require coddling, and his wife, the boxer and writer Sarah Deming, is better suited to all that, anyway. But Iverson is profuse with the couple of things he enjoys outside of music — namely, Twitter, where he is an exuberant presence, and crime fiction, which he reads prolifically and writes epic essays about for Do The Math. Turns out the stuff is quite jazzy.

‘Traditionally I play much slower than my peers. I always wanted to make sure I had a belief in every note.’

“If you hear a classic ’50s or ’60s instrumental,” Iverson explains, “the frame is very clear. There’s a lot of innovation happening, but essentially you’re going to play the blues and there are going to be some horn solos and the rhythm section is gonna swing. The same thing if I pick up a book I haven’t read by one of my favorite crime fiction authors. I’m going to get a great variation on a form I know and understand.”

Few have played with form and variation to such tantalizing — and amusing — effect as The Bad Plus. Asked about the place of humor in serious music, Iverson frets that his answer will sound pompous.

“I think the key element to something that’s witty or funny is surprise,” he says. “I can hear Thelonious Monk play piano, and I might have a belly laugh. But it’s because I’ve spent enough time learning what’s expected, so when something is unexpected I shake my head in disbelief.”

That, of course, is also the beauty of jazz virtuosos exploding a Johnny Cash tune. We know what’s expected, and shake our heads in disbelief.